Dust Absorption and the Ultraviolet Luminosity Density atz ≈ 3 as Calibrated by Local Starburst Galaxies

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Abstract
We refine a technique to measure the absorption corrected ultraviolet (UV) luminosity of starburst galaxies using rest frame UV quantities alone, and apply it to U-dropouts at z ~ 3 found in the Hubble Deep Field. The method is based on an observed correlation between the ratio of far infrared (FIR) to UV fluxes with spectral slope \beta (a UV color). A simple fit to this relation allows the UV flux absorbed by dust to be calculated, and hence the dust-free UV luminosity to be determined. IUE spectra and IRAS fluxes of local starbursts are used to calibrate the ratio in terms of 1600 Angstrom absorption A_{1600}, and the transformation from broad band color to \beta. We show that the recent marginal and non-detections of HDF U-dropouts in the radio and sub-mm are consistent with our calculated A_{1600}. This is also true of observations of the ratio of optical emission line flux to UV flux density in the brightest U-dropouts. This latter ratio turns out not to be a good indicator of dust extinction. In U-dropouts, absolute magnitude correlates with \beta: brighter galaxies are redder, as is observed in local starburst galaxies. This suggests that a mass-metallicity relationship is in place by z ~ 3. The UV luminosity function of U-dropouts extends up to M_{1600,0} ~ -24 ABmag corresponding to a star formation rate ~ 200 \Msun/yr (H_0 = 50 km/s/Mpc, q_0 = 0.5). The absorption-corrected UV luminosity density at z ~ 3 is \rho_{1600,0} => 1.4x10^{27} erg/s/Hz/Mpc^3; still a lower limit since completeness corrections have not been done and because only galaxies with A_{1600} < ~3.6 mag are blue enough to be selected as U-dropouts. The luminosity weighted mean dust absorption factor of our sample is 5.4 +/- 0.9$ at 1600\AA (abridged).Comment: ApJ accepted. 22 pages, 7 figure
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